Carnivorous aquatic Utricularia species catch small prey animals using millimetre-sized underwater suction traps, which have fascinated scientists since Darwin's early work on carnivorous plants. Suction takes place after mechanical triggering and is owing to a release of stored elastic energy in the trap body accompanied by a very fast opening and closing of a trapdoor, which otherwise closes the trap entrance watertight. The exceptional trapping speed--far above human visual perception--impeded profound investigations until now. Using high-speed video imaging and special microscopy techniques, we obtained fully time-resolved recordings of the door movement. We found that this unique trapping mechanism conducts suction in less than a millisecond and therefore ranks among the fastest plant movements known. Fluid acceleration reaches very high values, leaving little chance for prey animals to escape. We discovered that the door deformation is morphologically predetermined, and actually performs a buckling/unbuckling process, including a complete trapdoor curvature inversion. This process, which we predict using dynamical simulations and simple theoretical models, is highly reproducible: the traps are autonomously repetitive as they fire spontaneously after 5-20 h and reset actively to their ready-to-catch condition.